Physics misconception

I have a question: if a roller coaster is gowing around a track, what is keeping it from falling down at the top? I know there is no "force" pulling it up, but how could i write an equation to measure that pull (acceleration)?

Staff: Mentor

T@P said:

true, but is there a way to calculate the force acting up on the roller coaster at the apex of its revolution?

I assume you are talking about a coaster going upside down in a loop-the-loop fashion? If so, realize that the coaster is undergoing centripetal acceleration downward. So identify the forces on the coaster and use Newton's 2nd law.

Staff: Mentor

The forces at the top would be mg down and the normal force also down. How does it stay up...?

Inertia---It's moving! It "stays" up the same way a ball on the end of a string stays up if you were to swing it overhead. (It doesn't really stay up there---it goes around and back down.)

If there were no forces acting on the coaster, it would just keep moving in a straight line. If only gravity acted, it would assume a parabolic trajectory. But the track also exerts a force making it go in a tighter circle. Assuming the coaster is not attached to the track (of course it is!), if the speed is too low, it will fall off the track!

I understand the idea, but what keeps it up would be the velocity? but isnt the velocity perpendicular to the force of gravity and therefore have no effect on it? Im sorry if I appear slow and thank you for your help, but i simply dont understand how I could draw a freebody diagram of an object at the top of a roller coaster and see that it does not fall down?

Staff: Mentor

T@P said:

I understand the idea, but what keeps it up would be the velocity? but isnt the velocity perpendicular to the force of gravity and therefore have no effect on it? Im sorry if I appear slow and thank you for your help, but i simply dont understand how I could draw a freebody diagram of an object at the top of a roller coaster and see that it does not fall down?

But it does fall down! It is accelerated downward due to the forces on it. (Keep in mind that a force is need to change a velocity, not cause a velocity.) It doesn't fall straight down, since it does have a sideways velocity.

And why would you think gravity would not affect something just because it is moving sideways? (True, it would not affect the horizontal speed, but it would certainly change the vertical.)

The free body diagram is easy. The only forces, as you noted, are the weight and normal force which both act down. And the acceleration is down, so it all makes sense. Note that if the curve of the track is stronger (smaller radius) than the parabolic arc of a free projectile, that the track must push down on the coaster to force it to follow the track--that's the normal force.

This is the same as a centrifuge. Spins everything around and around at high speeds, heavier masses going more vertical, lower mass sinking to the bottom. This is from the centrifugal force giving off a greater force than that of gravity.